General Mathematics

Why Does Possibility Exist

Why does possibility exist and where does it come from? These are questions not usually asked because possibility is so deeply woven into the fabric of the universe we take its existence completely for granted. By exploring a well known, but essentially unexamined absolute first principle, we describe why possibility exists, where it comes from and the form it takes in our universe. We describe the fundamental mechanism which enables possibility to exist and to resolve to choice in context, which means we also generate the existence of context and choice. We discuss a number of examples to demonstrate how this mechanism operates and what it means.

In the late 19th Century, paradoxes revealed that no true universal set, no true set of all sets, can exist. Axiomatic set theory was developed as the solution to the problem this impossibility presented and the impossibility was treated as a failure of the naive conception of set theory and was set aside. We do not address set theory except in passing. Set theory assumes possibility exists to describe which sets are possible. We look instead directly at the meaning of the impossibility uncovered by the paradoxes to uncover why possibility itself can exist. This has never been done. We show that deriving without assumptions from this impossibility generates a specific structure which enables the existence of possibility, context and choice.

We begin by explaining the process by which we focused on this impossibility; we describe the process by which we can answer a question so obvious we take it for granted. We then derive the existence of possibility, context and choice and define the inherent structure we call the Choice Mechanism. To use a metaphor from the paper, we describe a box whose sides are absolute impossibility and which can be filled with all the possibility that can exist. By structure, we mean an actual structure in which possibility occurs and through which all resolution of possibility happens.

The rest of the paper consists of five discussion groups. We present in these a number of illustrative examples all of which cannot currently be explained. To be clear, we use the Choice Mechanism to provide the missing "why" for a number of otherwise unexplainable, fundamental phenomena, with each discussion group covering a major aspect of how this underlying structure for possibility appears and operates.

1. The first group explains how the Choice Mechanism calculates: we explain why numbers exist, meaning both Base 2 and Base 10, why the fundamental analytic constant e, the base of natural logarithms, exists and why functions exist. Again to be clear, we mean we derive the actual existence of numbers, of e and of function. We show in this and other sections how the universe actually calculates possibilities and how those become results.
2. The second group discusses physical examples which literally manifest the Choice Mechanism context structure; we explain why the logarithmic spiral occurs in nature and how the context structure of the Choice Mechanism completely explains certain fundamental behaviors of elementary particles.
3. The third group focuses on how the Choice Mechanism context structure operates, specifically on how coherent resolution to choice of context expresses as a force; we explain why natural selection and economic “markets” exist.
4. The fourth discusses fundamental aspects of how the Choice Mechanism acts on persistent structures, meaning how coherence interacts with things that have a past, present and future. This section contains too many examples to list.
5. The fifth discussion group describes how the Choice Mechanism functions at scale, meaning the effects of coherent resolution of context to choice at various scales of existence: we explain why the arrow of time exists and why the subjective experience of time exists. We also explain why and how constants of infinite depth can exist in a universe in which time exists.

Please understand this work completely agrees with established fact and theory, does not in any way rely on "hidden variables" or new particles or forces, and is not in any way mystical. We do not advance any new paradigms. We merely explain what we in essence already know: that possibilities exist and that somehow these come together to make our universe and all that happens in it. We provide the missing “why”. We understand this is difficult to believe. You have to read it. We can't otherwise persuade you.

The material is presented in a non-technical manner. The math is trivial.

No contact information is provided because we prefer to remain unknown.

Submission history

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